pin: the question as you so nicely danced around it is between armor and stealth.
#1 stealth on ships do NOT work, they are not invisible, there was a phase in tank development the leopard 1 is a prime example with the same school of thought, we can see them first and shoot'em first, they came up with 'nah, this shit do not work, lets put some armor back on.' there have however been no naval engagements to prove either way, but my gut feeling is some armor is better than no armor, and it will be a bloody massacre.
#2 lowered RCS or other signatures is all good and well...but not if it breaks EVERYTHING else(zumwalt), and my argument is that it is of questionable advantage compared to armor, the one does not exactly exclude the other though.
nemo: and at what standoff range would a zumwalt be wrecked? that armor at least gives the ship some distance to shoot the missile down, now, we do not know the exact numbers on the effects of nukes, but crossroads gives us a ballpark, given that piggie outside the turret died 2 days later the initial thermal/kinetic waves did not kill it...
found a little program that might be reasonably accurate.
http://nuclearsecrecy.com/nukemap/
500 REM range is about 5 Gy, so for a shipwreck(upper estimate, 500kt) against a unarmored ship, about 2.2km, that gives us a number to work with to figure out initial radiation burst.
so assuming these numbers, a shipwreck at 150m would dish out 1075.5Gy, so about eleven inch of steel(or less of more advanced stuffs, lets say 12 for good measure) would do the trick, problem is it would have to be omni directional, thereby heavy as bloody hell, but doable.
and on the under ship explosion, assuming it explodes UNDER the ship, and throws it up, given enough depth and tough enough sealed vessel, it should just bob back up a bit worse for wear, not exactly under? push it to the side, most of the ships in Baker shot survived just fine....the question is crew survivability, difficult to be sure here, but probably tricky.
so a 12 inch armor(as long as it is from the side, Iowa would qualify with 12.1 inch belt armor) could survive a shipwreck at 150m, a zumwalt would suffer crew death at 2km.
no armor is effing stupid.